If you want dead simple regulations, require that banks publish their balance sheet. (Perhaps with a bit of a lag, if you want to give them the opportunity to have some trade secrets. But easier to just ask for all current balance sheet items to be public.)
Without deposit insurance customers will take a flight to quality. Or see https://www.bloomberg.com/view/articles/2014-08-27/lending-c... for how banks might want to make assets match liabilities.
Reinsurance companies might offer private deposit insurance for a fee to banks with good enough balance sheets.
Right now we have regulators require a minimum quality of balance sheets, but also giving an explicit and implicit guarantees that deposits with banks that meet that minimum quality will not go down. What I want to do is remove that minimum, replace it with more transparency instead, and remote the guarantee.
Argument stolen from this book http://www.independent.org/publications/tir/article.asp?a=51...
The author is obsessed with figuring out simple regulations that only require a few competent and honest civil servants to implement. That's because competent and honest civil servants are one of the most precious resource.
For privatizing companies he suggests: just auction off the company to the highest cash bidder. (If the winner wants to take the former state company public, that's there choice.)
For bankruptcy: if creditors and debtor company can't agree on restructuring, just liquidate the company in an auction. (Court ordered debt restructuring takes up precious civil servants, and invites corruption.)
The author actually describes the how and why and historical background. He's actually worked in the field.
One way is to just regulate banks like any other business without any special laws for them.